When used as a verb they both have the same general meaning of “to move upwards”, the main difference is that rise is an intransitive verb (it does not take an object), while raise is a transitive verb (it requires an object):
As you can see from these examples, (nobody is pushing up the sun!), whereas (Mary moved her hand upwards/The government make laws to increase taxes).
rise (v) Something rises by itself
The sun rises in the east.
The chairman always rises to the occasion.
I will rise tomorrow morning at 6 a.m. to walk the dog.
Rise is an irregular verb: rise / rose / risen
raise (v) Something else is needed to raise something.
Lynne raised her hand.
The government is going to raise taxes.
They can’t raise the Titanic.
Raise is a regular verb: raise / raised / raised